Problem: Solve for $x$ and $y$ using elimination. ${5x+6y = 52}$ ${6x+5y = 47}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $6$ ${-25x-30y = -260}$ $36x+30y = 282$ Add the top and bottom equations together. $11x = 22$ $\dfrac{11x}{{11}} = \dfrac{22}{{11}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {5x+6y = 52}\thinspace$ to find $y$ ${5}{(2)}{ + 6y = 52}$ $10+6y = 52$ $10{-10} + 6y = 52{-10}$ $6y = 42$ $\dfrac{6y}{{6}} = \dfrac{42}{{6}}$ ${y = 7}$ You can also plug ${x = 2}$ into $\thinspace {6x+5y = 47}\thinspace$ and get the same answer for $y$ : ${6}{(2)}{ + 5y = 47}$ ${y = 7}$